document.write( "Question 1147129: If the product of two consecutive even integers is increased by lesser integer, the result is 180. Find the integers. \n" ); document.write( "

Algebra.Com's Answer #768426 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "Let the two even integers be x and x+2. Then their product, increased by the smaller integer, is

\n" ); document.write( "x(x+2)+x = x^2+2x+x = x^2+3x

\n" ); document.write( "You want that expression to equal 180:

\n" ); document.write( " $\"x%5E2%2B3x+=+180\"$
\n" ); document.write( " $\"x%5E2%2B3x-180+=+0\"$

\n" ); document.write( "Solve by factoring. (I leave that to you....)

\n" ); document.write( "If a formal algebraic solution is not required, the answer can be found more quickly using trial and error.

\n" ); document.write( " $\"x%5E2%2B3x+=+180\"$
\n" ); document.write( " $\"x%28x%2B3%29+=+180\"$

\n" ); document.write( "Look for two integers whose difference is 3 and whose product is 180, with the restriction that the smaller number is even. The two numbers are 12 and 15.

\n" ); document.write( "So the smaller of the two even integers is 12 and the other is 14.

\n" ); document.write( "Note that, algebraically, the equation has two solutions, the other of which is -15. However, since the problem is about consecutive even integers, that solution has to be rejected. \n" ); document.write( "

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